document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1065983>Question 1065983</A>: <I><SPAN STYLE=\"word-break: break-all;\"> given: ABCE is an isosceles trapezoid with ray AB is parallel to ray EC, and ray AE is congruent to ray AD, prove: ABCD is a parallelogram </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #681169 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=681169\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> line of attack.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "see the attached picture.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you are given that ABCE is an isosceles trapezoid.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you are given that AB is parallel to EC.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this means that AE is congruent to BC.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you are given that AE and AD are congruent.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "triangle EAD is an isosceles triangle because AE and AD are congruent.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this means that angle 1 is equal to angle 3.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since angle 1 is equal to angle 2 and angle 3 is equal to angle 1, then angle 3 is also equal to angle 2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this means that AD and BC are parellel because their corresponding angles (angles 3 and 2) are equal.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since AB is parallel to EC and DC is part of the same line, than AB is parallel to DC.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you have AB parallel to DC and AD parallel to BC.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if opposite sides of a quadrilateral are parallel, then the quadrilateral is a parallelogram.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that might be able to do it,depending on whether all these statements are acceptable without proof.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "they are either postulates or theorems that have been previously proven.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if not, then you need to go a little deeper and prove some of the statements that you used..\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "here's my diagram.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/012901.jpg\" alt=\"$$$\" </>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this is not a formal proof, but should give you some ideas about how to proceed.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you can also prove that angle 4 is equal to angle 2 because they are alternate interior angles of parallel lines.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you can also prove that angle 6 is equal to angle 5 because they are alternate interior angles of parallel lines.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );